Session KA: Symmetries In Nuclei: In Honor of Rowe and Rosenteel

Static and Dynamic Properties of Medium-Mass and Heavy Nuclei: From Phenomenology to Microscopic Descriptions

Nuclear structure and reaction theory has seen tremendous advances in the past couple of decades. Innovative theory frameworks for describing the quantum-mechanical many-body system, increasingly powerful computational tools, and the prospect of confronting theory predictions with data on exotic unstable nuclei, have been driving the field. An important goal of the theory efforts is the move from phenomenological descriptions of nuclear properties to predictive theories based on microscopic frameworks. Throughout their careers, David Rowe and George Rosensteel delivered research works that were instrumental in making this transition. They provided connecting points between the phenomenology and microscopic approaches, making clever use of symmetry concepts that enabled technical breakthroughs and deep mathematical insights into successful descriptions of nuclei. I will discuss ongoing research aimed at integrating microscopic descriptions of nuclear structure into reaction predictions for medium-mass and heavy nuclei. I will highlight areas where Rowe and Rosensteel made important contributions and offer some thoughts on future directions.   

A Data View of Nuclear Symmetries

Symmetries in nuclei are generally introduced via mathematical properties of models and a

general applicability of the models to fitting data, but rigorous confrontation of the existence of

symmetries in nuclei with data is rare or non-existent. The well-established views of axially

symmetry (nuclear deformation) and quasispin SU(2) dynamical symmetry (many-body pairing

in spherical nuclei) are introduced and their limitations explored based on data. Less well-

established views, such as SO(5) symmetry and five-dimensional collective models, are then

sketched. A need to adhere more closely to a data-based view and simple models is urged;

complex and intricate models appear less tenable than simple mixing of configurations defined

by elementary models.   

Yang-Mills Theory for the Nuclear Collective Model

The primary goal of this discussion is to understand the dynamics of collective nuclear rotations. The main theoretical tool to achieve this goal is a gauge theory that uses a bundle connection. The bundle structure connects the angular and vortex degrees of freedom. The novel technique proposed for this research is the Yang-Mills theory of bundle connections. The character of nuclear rotations depends quantitatively on the connection between angular and vortex degrees of freedom. The Yang-Mills equation provides the correct equation for determining this connection. To this end, the underlying differential geometric relationship between Yang-Mills theory and the nuclear collective model will be discussed. Although similar mathematically, the underlying physics is substantially different. Minkowski space is the common base manifold for the Yang-Mills theories of electromagnetism and the electroweak forces; the corresponding gauge groups are U(1), SU(2)xU(1). The base manifold for the proposed Yang-Mills collective model is the space of nuclear rotations and quadrupole deformations; the gauge symmetry is SO(3), the group of vortex motions.